Stationary Solutions of a Mathematical Model for Formation of Coral Patterns

Lekam Watte Somathilake; Janak R. Wedagedera

doi:10.4236/am.2015.66100

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Applied Mathematics > Vol.6 No.6, June 2015

Stationary Solutions of a Mathematical Model for Formation of Coral Patterns ()

Lekam Watte Somathilake¹, Janak R. Wedagedera²

¹Department of Mathematics, Faculty of Science, University of Ruhuna, Matara, Sri Lanka.
²Simcyp-CERTARA Limited, Blades Enterprise Centre, Sheffield, UK.

DOI: 10.4236/am.2015.66100 PDF HTML XML 2,359 Downloads 2,728 Views

Abstract

A reaction-diffusion type mathematical model for growth of corals in a tank is considered. In this paper, we study stationary problem of the model subject to the homogeneous Neumann boundary conditions. We derive some existence results of the non-constant solutions of the stationary problem based on Priori estimations and Topological Degree theory. The existence of non-constant stationary solutions implies the existence of spatially variant time invariant solutions for the model.

Keywords

Reaction-Diffusion Equations, Stationary Solutions, Priori Estimates, Topological Degree Theory

Share and Cite:

Somathilake, L. and Wedagedera, J. (2015) Stationary Solutions of a Mathematical Model for Formation of Coral Patterns. Applied Mathematics, 6, 1099-1106. doi: 10.4236/am.2015.66100.

Conflicts of Interest

The authors declare no conflicts of interest.

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